We present the discovery of 12 apparently nonrepeating fast radio burst (FRB) sources, detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope. These sources, only one of which has been presented previously in the first CHIME/FRB catalog, were selected from a database comprising O(103) CHIME/FRB full-array raw voltage data recordings, based on their large signal-to-noise ratios and complex morphologies. Our study examines the time-frequency characteristics of these bursts, including drifting, microstructure, and periodicities. The events in this sample display a variety of unique drifting phenomenologies that deviate from the linear negative drifting phenomenon seen in many repeating FRBs, and motivate a possible new framework for classifying drifting archetypes. Additionally, we detect microstructure features of duration ≲50 μs in seven events, with some as narrow as ≃7 μs. We find no evidence of significant periodicities between subburst components. Furthermore, we report the polarization characteristics of seven events, including their polarization fractions and Faraday rotation measures (RMs). The observed ∣RM∣ values span a wide range of 17.24(2)–328.06(2) rad m−2, with apparent linear polarization fractions between 0.340(1) and 0.946(3). The morphological properties of the bursts in our sample appear broadly consistent with predictions from both relativistic shock and magnetospheric models of FRB emission, as well as propagation through discrete ionized plasma structures. We address these models and discuss how they can be tested using our improved understanding of morphological archetypes.